*4.1.7 Variance decomposition*

This analysis aims to measure the composition or contribution of the influence of each variable to other variables. This study focuses on looking at the influence of variables, including FDR, NPF, and BOPO. The findings of VDC are shown as follows.

**Table 10** shows the contribution of FDR, NPF, and BOPO toward FDR fluctuations. The findings suggest that FDR fluctuations are mainly influenced by FDR itself, even until the 10th period. Numerically, the shares of other variables are less than 10%. However, although the shares originated from NPF and BOPO are not dominant, any fluctuations of FDR are contributed by other variables. In other words, the liquidity risk existed in Islamic banks is insignificantly contributed by other risks, and it then implies Islamic banks frequently face liquidity problems in their balance sheets. In addition, these findings corroborate the previous findings suggested by impulse response that liquidity risk is negatively affected by financing and operational risks, which means it is mainly caused by liquidity itself (banks' balance sheet mismatch).

**Table 11** shows the variance decomposition of NPF due to the fluctuations from NPF itself, FDR, and BOPO. Empirically, the fluctuations of NPF initially are influenced by NPF itself. However, its composition gradually declines as other


#### **Table 10.**

*Variance decomposition of FDR.*

a. NPF which is the proxy of financing risk negatively responds shocks from FDR, but positively from BOPO. The former indicates that Islamic banks have conducted sound risk management practices, especially concerning with financing risk in the mid of higher financial intermediaries, while the latter indicates that Islamic banks have high sensitivity of financing risk due to failure in managing operational risk, such us human error, information

NPF—financing risk Negative (short run) Positive (short and long

**NPF FDR BOPO**

Positive (short run) and negative (long run)

runs)

Negative (short run) and positive (long run)

system, and standard operational procedure.

**Sensitivity of risk Shock originator**

and long runs)

and long runs)

*Impulse response BOPO to FDR. Source: Author's calculation.*

*Impulse response BOPO to NPF. Source: Author's calculation.*

FDR—liquidity risk Negative (short

BOPO—operational risk Positive (short

*Source: Author's calculation.*

*Summary of impulse response results.*

**Table 9.**

**66**

**Figure 7.**

*Banking and Finance*

**Figure 8.**


**Table 13** shows the summary of variance decomposition function at the 10th period. The findings suggest that the main risk that triggers Islamic bank is liquidity risk, while other risks that show the highest contribution toward risk vulnerability are financing risk and operational risk. Therefore, Islamic banks will always face these risks, and they are categorized as the core or main risk in Islamic banks,

NPF 76.93120 0.269536 22.80826 FDR 3.623686 90.52347 5.852848 BOPO 46.13966 1.172802 52.68754

**NPF FDR BOPO**

**Dependent variables Independent variables**

*The summary of variance of decomposition at the 10th period (%).*

The Granger causality test is used to determine the causal relationship of each variable with other variables. The test level used in the Granger causality test is the level of confidence (α = 0.05) with lag length 2, according to the optimal lag length that has been done previously. Results of the Granger causality test are as follows. **Table 14** shows the causality between variables with various probability values. The findings suggest that the variables have one-directional relationship, namely:

a. There is one-directional relationship between NPF and FDR. It means that the vulnerability in Islamic banks due to liquidity risk is empirically caused by financing risk. This finding strengthens the previous findings obtained through VECM estimation and IRF that financing risk affects the liquidity

b. There is one-directional relationship between BOPO and FDR. It means that the vulnerability in Islamic banks due to liquidity risk is empirically caused by operational risk. This finding corroborates the previous findings that liquidity

**NPF does not Granger cause FDR 5.44792 0.0057** FDR does not Granger cause NPF 1.67488 0.1927 **BOPO does not Granger cause FDR 7.97421 0.0006** FDR does not Granger cause BOPO 0.16992 0.8440 BOPO does not Granger cause NPF 2.40254 0.0959 **NPF does not Granger cause BOPO 4.91669 0.0092**

**f-Statistic Prob**

risk though its relationship is negative and small.

**H0 Lag 2**

particularly in Indonesia.

*Source: Author's calculation. 1% level of significance*

*The Granger causality test.*

**Table 14.**

**69**

*Source: Author's calculation.*

*Risk Analyses on Islamic Banks in Indonesia DOI: http://dx.doi.org/10.5772/intechopen.92245*

**Table 13.**

*4.1.8 The Granger causality test*

#### **Table 11.**

*Variance decomposition of NPF.*

variables'shares gradually increase. On the 10th period, the share of NPF stands for 76.93, FDR remains small, but BOPO shares a majority portion around 22.8. These findings imply that financing risk frequently occurs in Islamic banks, and this risk is quite large contributed by the operational risk. In addition, the results strengthen the previous findings obtained through impulse response that financing risk is empirically triggered by operational risk.

**Table 12** shows the variance decomposition of BOPO. Empirically, the results suggest that initially the fluctuation on BOPO is contributed by BOPO itself, but gradually other variables influence it. Until the 10th period, BOPO fluctuations are dominantly attributed by NPF for around 46.42%, but with a negligible portion of FDR. It implies that operational risk in Islamic banks is mainly contributed by financing risk and a small portion from liquidity risk.


#### **Table 12.**

*Variance decomposition of BOPO.*


#### **Table 13.**

variables'shares gradually increase. On the 10th period, the share of NPF stands for 76.93, FDR remains small, but BOPO shares a majority portion around 22.8. These findings imply that financing risk frequently occurs in Islamic banks, and this risk is quite large contributed by the operational risk. In addition, the results strengthen the previous findings obtained through impulse response that financing risk is

**Period SE FDR NPF BOPO** 0.301986 1.284774 98.71523 0.000000 0.375125 0.886743 98.61763 0.495627 0.416529 0.785144 98.59483 0.620030 0.517248 0.513238 94.73262 4.754143 0.579325 0.428273 90.02078 9.550951 0.624881 0.380940 86.74632 12.87274 0.691786 0.319991 83.37349 16.30652 0.742180 0.297634 80.39042 19.31195 0.784787 0.277975 78.41862 21.30341 0.834778 0.269536 76.93120 22.80826 Total average 0.5868625 0.5444248 88.654114 10.8023631

**Table 12** shows the variance decomposition of BOPO. Empirically, the results suggest that initially the fluctuation on BOPO is contributed by BOPO itself, but gradually other variables influence it. Until the 10th period, BOPO fluctuations are dominantly attributed by NPF for around 46.42%, but with a negligible portion of FDR. It implies that operational risk in Islamic banks is mainly contributed by

**Period SE FDR NPF BOPO** 2.927100 0.357969 2.680542 96.96149 3.735015 0.265543 5.788679 93.94578 4.198097 0.466521 10.22600 89.30747 4.645547 0.781165 19.34129 79.87754 5.026835 0.754420 25.87602 73.36956 5.431698 0.777258 32.08065 67.14209 6.226521 0.940389 37.36899 61.69062 6.226521 1.003506 40.89494 58.10156 6.612534 1.089031 43.87340 55.03757 6.985251 1.172802 46.13966 52.68754 Total average 5.2015119 0.7608604 26.4270171 72.812122

empirically triggered by operational risk.

*Sources: Author's calculation.*

*Banking and Finance*

*Variance decomposition of NPF.*

*Sources: Author's calculation.*

*Variance decomposition of BOPO.*

**Table 12.**

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**Table 11.**

financing risk and a small portion from liquidity risk.

*The summary of variance of decomposition at the 10th period (%).*

**Table 13** shows the summary of variance decomposition function at the 10th period. The findings suggest that the main risk that triggers Islamic bank is liquidity risk, while other risks that show the highest contribution toward risk vulnerability are financing risk and operational risk. Therefore, Islamic banks will always face these risks, and they are categorized as the core or main risk in Islamic banks, particularly in Indonesia.
